Department of mathematics
Federal University of Paraná
19081, Curitiba, Brazil
email: clebermedeira@ufpr.br
Cleber de Medeira
Abstract:
In this article, we consider a class of involutive systems of n
smooth vector fields on the torus of dimension n+1. We prove that
the global solvability of this class is related to an
algebraic condition involving Liouville forms and the connectedness
of all sublevel and superlevel sets of the primitive of a certain
1-form associated with the system.
Submitted April 19, 2013. Published November 8, 2013.
Math Subject Classifications: 35N10, 32M25.
Key Words: Global solvability; involutive systems;
complex vector fields; Liouville number.
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Cleber de Medeira Department of mathematics Federal University of Paraná 19081, Curitiba, Brazil email: clebermedeira@ufpr.br |
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